This partially randomized phase II/III trial studies how well cisplatin and combination chemotherapy works in treating children and young adults with hepatoblastoma or liver cancer after surgery. Drugs used in chemotherapy, such as cisplatin, doxorubicin, fluorouracil, vincristine sulfate, carboplatin, etoposide, irinotecan, sorafenib, gemcitabine and oxaliplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving combination chemotherapy after surgery may kill more tumor cells.